Autogyro, gyroplane, gyrocopter  - call it  what you will, but the strictly correct term is autogyro.

A few facts

Whilst autogyros may look like small helicopters they are actually quite unlike them.  The rotor blades of a helicopter are driven by its engine; the rotorblades of the autogyro are completely free wheeling, being driven solely by the wind going through them.  This free spinning of the blades is called autorotation.  In a helicopter the air is drawn downwards through its blades;  in an autgyro the air goes upwards through the blades.

The whole autogyro body is hanging on just one bolt, commonly called the Jesus bolt  - for obvious reasons.

Autogyros are far less affected by unstable air and wind gusts than small fixed wing aeroplanes.  They are much more comfortable to fly in strong or gusty winds and can fly safely in conditions that would cause problems for small aeroplanes.

From the ground it looks like the rotor blades are simply going round and round.  If that’s all they did, the autogyro would roll over and crash.    In fact, the blades  are  constantly moving up and down as well as changing  the angle at which they go though the air.  

The autogyro cannot stall like an aeroplane.  As long as the pilot ensures that air is always coming at the blades from underneath, the blades will keep turning of their own accord.  

They have the ability to fly very slowly without losing height, simply sinking slowly when the speed through the air is insufficient (20 to 30 mph).  In a medium to strong wind they can readily hold their position over the ground, effectively hovering.